In the present specification, reference is made to the following publications cited for illustrating prior art techniques.    1. Hasegawa, A. & Tappert, F. Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion. Appl. Phys. Lett. 23, 171-172 (1973).    2. Hasegawa, A. & Kodama, Y. Signal Transmission by Optical Solitons in Monomode Fiber. Proc. IEEE 69, 1145-1150 (1981).    3. Herr, T. et al. Temporal solitons in optical micro-resonators. Nat. Photonics 8, 145-152 (2013).    4. Brasch, V. et al. Photonic chip-based optical frequency comb using soliton Cherenkov radiation. Science 351, 357-360 (2015).    5. Bozinovic, N. et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545-1548 (2013).    6. Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 6, 488-496 (2012).    7. Puttnam, B. J. et al. 2.15 Pb/s Transmission Using a 22 Core Homogeneous Single-Mode Multi-Core Fiber and Wideband Optical Comb. In European Conference on Optical Communications, paper PDP3.1 (2015).    8. Dai, D. & Bowers, J. E. Silicon-based on-chip multiplexing technologies and devices for Peta-bit optical interconnects. Nanophotonics 3, 283-311 (2014).    9. Mollenauer, L. F., Stolen, R. H. & Gordon, J. P. Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys. Rev. Lett. 45, 1095-1098 (1980).    10. Haus, H. A. & Wong, W. S. Solitons in optical communications. Rev. Mod. Phys. 68, 423-444 (1996).    11. Möbius, P. Hasegawa, A. Kodama, Y.: Solitons in Optical Communications. Oxford, Clarendon Press 1995. XIV.    12. Nakazawa, M., Yamada, E., Kubota, H. & Suzuki, K. 10 Gbit/s Soliton Data Transmission over One Million Kilometres. Electron. Lett. 27, 1270-1272 (1991).    13. Hillerkuss, D. et al. 26 Tbit s−1 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing. Nat. Photonics 5, 364-371 (2011).    14. Ataie, V. et al. Ultrahigh Count Coherent WDM Channels Transmission Using Optical Parametric Comb Based Frequency Synthesizer. J. Light. Technol. 33, 694-699 (2015).    15. Hillerkuss, D. et al. Single-Laser 32.5 Tbit/s Nyquist WDM Transmission. J. Opt. Commun. Netw. 4, 715-723 (2012).    16. Temprana, E. et al. Overcoming Kerr-induced capacity limit in optical fiber transmission. Science 348, 1445-1448 (2015).    17. Weimann, C. et al. Silicon-organic hybrid (SOH) frequency comb sources for terabit/s data transmission. Opt. Express 22, 3629 (2014).    18. Pfeifle, J. et al. Flexible terabit/s Nyquist-WDM super-channels using a gain-switched comb source. Opt. Express 23, 724 (2015).    19. Vujicic, V. et al. Quantum Dash Passively Mode-Locked Lasers for Tbit/s Data Interconnects. In Optical Fiber Communication Conference, paper Tu3I.4 (OSA, 2015).    20. Hu, H. et al. Single-Source AlGaAs Frequency Comb Transmitter for 661 Tbit/s Data Transmission in a 30-core Fiber. In CLEO: 2016 Postdeadline Paper Digest JTh4C. 1 (OSA, 2016).    21. Kemal, J. N. et al. Parallel Multi-Wavelength Intradyne Reception Using an Optical Frequency Comb as a Local Oscillator. In ECOC Proceedings P. 4.18 (2015).    22. Del'Haye, P. et al. Optical frequency comb generation from a monolithic micro-resonator. Nature 450, 1214-7 (2007).    23. Levy, J. S. et al. CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects. Nat. Photonics 4, 37-40 (2009).    24. Herr, T. et al. Universal formation dynamics and noise of Kerr-frequency combs in micro-resonators. Nat. Photonics 6, 480-487 (2012).    25. Kippenberg, T. J., Holzwarth, R. & Diddams, S. A. Micro-resonator-Based Optical Frequency Combs. Science 332, 555-559 (2011).    26. Xue, X. et al. Mode-locked dark pulse Kerr combs in normal-dispersion micro-resonators. Nat Phot. 9, 594-600 (2015).    27. Dong, P. et al. Monolithic Silicon Photonic Integrated Circuits for Compact 100+Gb/s Coherent Optical Receivers and Transmitters. IEEE J. Sel. Top. Quantum Electron. 20, 1-8 (2014).    28. Azadeh, S. S. et al. Low V Silicon photonics modulators with highly linear epitaxially grown phase shifters. Opt. Express 23, 23526 (2015).    29. Liang, D. & Bowers, J. E. Recent progress in lasers on silicon. Nat. Photonics 4, 511-517 (2010).    30. Wang, Z. et al. Room Temperature InP DFB Laser Array Directly Grown on (001) Silicon. Nat. Photonics 9, 837-842 (2015).    31. Pfeifle, J. et al. Coherent terabit communications with micro-resonator Kerr frequency combs. Nat. Photon. 8, 375-380 (2014).    32. Pfeifle, J. et al. Full C and L-Band Transmission at 20 Tbit/s Using Cavity-Soliton Kerr Frequency Combs. In CLEO: 2015 Postdeadline Paper Digest JTh5C.8 (OSA, 2015).    33. Haelterman, H., Trillo, S. & Wabnitz, S. Dissipative modulation instability in a nonlinear dispersive ring cavity. Opt. Commun. 91, 401-407 (1992).    34. Akhmediev, N. Dissipative Solitons: From Optics to Biology and Medicine. (Springer, 2008).    35. Yi, X., Yang, Q.-F., Yang, K. Y., Suh, M.-G. & Vahala, K. Soliton frequency comb at microwave rates in a high-Q silica micro-resonator. Optica 2, 1078 (2015).    36. Kachris, C. & Tomkos, I. A survey on optical interconnects for data centers. IEEE Commun. Surv. Tutorials 14, 1021-1036 (2012).    37. Lugiato, L. A. & Lefever, R. Spatial Dissipative Structures in Passive Optical Systems. Phys. Rev. Lett. 58, 2209 (1987).    38. Karpov, M. et al. Universal dynamics and controlled switching of dissipative Kerr solitons in optical micro-resonators. at arXiv:1601.05036 (2016).    39. Yi, X., Yang, Q., Ki, Y. Y. & Vahala, K. Active capture and stabilization of temporal solitons in micro-resonators. Opt. Lett. 41, 2037-2040 (2016)    40. 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Optical solitons are waveforms that preserve their shape while travelling, relying on a balance of dispersion and nonlinearity1,2. Data transmission schemes using solitons were heavily investigated in the 1980's promising to overcome the limitations imposed by dispersion of optical fibers. These approaches, however, were eventually abandoned in favour of wavelength-division multiplexing (WDM) schemes, that are easier to implement and offer much better scalability to higher data rates. Optical solitons may experience a comeback in optical terabit communications, this time not as a competitor, but as a key element of massively parallel WDM. Instead of encoding data on the soliton itself, continuously circulating solitons in Kerr-nonlinear micro-resonators can be exploited to generate broadband optical frequency combs3,4.
The first observation of solitons in optical fibers9 in 1980 was immediately followed by major research efforts to harness such waveforms for long-haul communications beyond the limits imposed by chromatic dispersion in optical fibers10,11. In these schemes, data was encoded onto a soliton pulse train by simple amplitude modulation using on-off-keying (OOK). However, even though the viability of the approach was experimentally demonstrated by transmission of data streams over one million kilometres12, the vision of soliton-based communications was ultimately hindered by difficulties in achieving shape-preserving propagation in real transmission systems10. Moreover, with the advent of wavelength-division multiplexing (WDM), line rates in long-haul communication systems could be increased by rather simple parallel transmission of data streams with lower symbol rates, for which dispersion represents much less of a problem. As a consequence, soliton-based communication schemes have moved out of focus over the last two decades.
More recently, frequency combs were demonstrated to hold promise for revolutionizing high-speed optical communications, offering tens or even hundreds of well-defined narrowband optical carriers for massively parallel WDM7,13-15. Unlike carriers derived from a bank of individual laser modules, the tones of a comb are intrinsically equidistant in frequency, thereby eliminating the need for individual wavelength control of each carrier and for inter-channel guard bands7,15. In addition, stochastic frequency variations of the carriers are strongly correlated, which enables efficient compensation of impairments caused by nonlinearities of the transmission fiber16.
For application in optical communications, frequency comb sources must be integrated into ultra-compact transmitter and receiver systems. Over the last years, a wide variety of chip-scale frequency comb sources have been demonstrated, including modulator-based comb generators17, as well as gain-switched18 or mode-locked lasers19. These schemes, however, provide only restricted numbers of carriers, and the highest data rate demonstrated with such chip-scale comb sources19 so far amounts to 2.3 Tbit/s. Transmission at higher data rates7,13-15,20, still relies on spectral broadening of narrowband seed combs using dedicated optical fibers7,13-15 or nanophotonic waveguides20 with high Kerr nonlinearities. However, to generate uniform comb spectra with broadband spectral envelopes, these schemes often rely on delicate dispersion management schemes, often in combination with intermediate amplifiers.14 Such schemes are difficult to miniaturize and not amenable to chip-scale integration. Moreover, with a few exceptions at comparatively low data rates21, all advanced comb-based transmission experiments still rely on conventional continuous-wave lasers as optical local oscillators (LO) for coherent detection. As a consequence, these concepts exploit the scalability advantages of frequency combs for massively parallel optical communications only at the transmitter, but not at the receiver side.
Dissipative Kerr solitons (DKS)3 generated in photonic chip based micro-resonators can overcome these limitations. In general, Kerr comb sources22-26 offer unique advantages such as small footprint, large number of optical carriers with narrow optical linewidths, and line spacings of tens of GHz, which can be designed to fit established WDM frequency grids. Moreover, the approach allows to leverage the tremendous advances in silicon photonic integration, enabling advanced multiplexer circuits8, on-chip detectors27, modulators28, and lasers29,30. Using low-noise Kerr combs, coherent data transmission was demonstrated previously31, but the aggregate line rate was limited to 1.44 Tbit/s due to strong irregularities of the optical spectrum associated with the specific comb states. This restricted the number of usable WDM carriers and led to relatively low optical powers, such that rather simple quadrature phase-shift keying (QPSK) had to be used as a modulation format.
Using in particular micro-resonator soliton Kerr frequency combs can overcome these limitations of conventional Kerr comb sources, thereby unlocking the tremendous potential of Kerr comb sources for massively parallel high-speed data transmission32. Dissipative Kerr soliton (DKS) comb states are distinct from previously studied Kerr combs in that their waveform corresponds to continuously circulating optical pulses in the time domain that lead to extraordinarily smooth and broadband spectral envelopes. Theoretically predicted in Refs. 33 and 34, DKS have been observed in a different types of micro-resonators including silica-on-silicon35, silicon nitride4 (Si3N4) as well as crystalline MgF2 devices3.
In Ref 32, integrated Si3N4 micro-ring resonators have been used to perform a series of proof-of-concept demonstrations that exploit the extraordinarily smooth and broadband spectral envelope and the inherently low phase noise of soliton Kerr combs. The devices feature free spectral ranges of approximately 100 GHz and intrinsic Q-factors of approximately 106. The Si3N4 platform was chosen because of its remarkable reliability and its compatibility with large-scale silicon-based processing23. According to Ref. 32, data have been transmitted on 94 carriers that span the entire telecommunication C and L bands with a free spectral range (FSR) of approximately 100 GHz. Using 16-state quadrature amplitude modulation (16QAM) at a symbol rate of 40 GBd, an aggregate line rate (net data rate) of 30.1 Tbit/s (28.0 Tbit/s) was achieved.
Broadband Kerr comb generation using dissipative Kerr solitons in high-Q silicon nitride micro-resonators is illustrated in FIG. 1. Kerr comb sources rely on parametric frequency conversion in high-Q micro-resonators, which are pumped by a continuous-wave (cw) laser22,25. The principle of comb generation is shown in FIG. 1A: The micro-resonator is driven by a tunable cw-laser and a high-power erbium-doped fiber amplifier (EDFA). After the micro-resonator, a notch filter (NF) supresses the remaining pump light. Lensed fibers are used to couple light in and out of the on-chip waveguides. A fiber polarization controller (FPC) is adjusted for maximum coupling into the resonance. The insets show the scanning electron microscopy (SEM) images of a dispersion optimized Si3N4 micro-resonator with radius 240 μm. Right inset shows the whole resonator. Left insets show the cross sections of the ring resonator's waveguide (dimensions 0.8×1.65 μm2) at the coupling point (upper inset) and at the tapered section (lower inset, dimensions 0.8×0.6 μm2). The tapered section is responsible of filtering higher order modes families43 while preserving a high quality factor (Q˜106) for the two fundamental modes TE00 and TM00.
FIG. 1B shows the power spectra and time-domain representation of different low-noise Kerr frequency comb states: Single-soliton Kerr combs (top) exhibit a short soliton pulse circulating inside the cavity. This leads to a broadband comb spectrum with smooth envelope that is perfectly suited for high-speed data transmission. Such comb states are obtained for pump wavelengths above the thermally shifted resonance wavelength of the cavity (“effective red detuning”). In contrast to that, Kerr com generators of previous transmission experiments (bottom) were operated with and effectively blue detuned pump, leading to a periodic waveform which does not exhibit any discrete pulses in the time domain. The corresponding spectra exhibit substantial variations of the power distribution, thereby limiting performance of the associated data transmission schemes.
According to FIG. 1C, the measured spectrum of a single-soliton frequency comb shows that the frequency comb presents a smooth envelope with a 3 dB bandwidth of 6 THz with hundreds of carriers which cover in excess both C and L telecommunication bands, highlighted in red and blue respectively.
Dissipative Kerr solitons represent a particularly attractive subset of Kerr comb states. They appear as specific solutions of the Lugiato-Lefever equation37 and consist of an integer number of discrete secant-hyperbolic shaped pulses circulating in the cavity3. DKS rely on the double balance of dispersion and Kerr nonlinearity, as well as of parametric gain and cavity loss. The number of solitons in the cavity can be adjusted by fine-tuning of the pump wavelength3,38.
Of particular interest are the single-soliton combs states, which consist of only one ultra-short pulse circulating around the cavity, leading to a broadband comb spectrum with smooth numerically predictable3 envelope, see upper panel of FIG. 1B. The measured power spectrum of the DKS comb state is shown in FIG. 1C, obtained at the output of the notch filter (NF) of FIG. 1A. This is in sharp contrast to conventional Kerr frequency combs for which the intra-cavity waveform corresponds to a periodic pattern, which does not exhibit any discrete pulses, see lower panel of FIG. 1B. The spectra of these patterns also consist of discrete equidistant lines, but exhibit substantial variations of the spectral power distribution, which severely limits the number of carriers that can be used for WDM transmission31.
DKS frequency combs can be generated by operating the resonator in the effectively red-detuned regime with respect to the cavity resonance, where the pump wavelength is bigger than the wavelength of the thermally shifted resonance3. This regime can be accessed by fast sweeping of the pump laser through the cavity resonance from a blue-detuned wavelength to a predefined red-detuned wavelength3,4. Importantly, once a multiple-soliton comb state is generated, the transition to a single-soliton state can be accomplished in a reliable and deterministic manner as recently reported38. The soliton comb states are remarkably robust and remain stable for many hours in a laboratory environment without requiring any feedback control mechanisms39.
DKS frequency comb based signal processing still may have limitations in terms of achievable data rate and/or device and processing complexity on the receiver side.